The report will look in closer detail at how hosting the games could work.
It will consider the kinds of venues and transport links required, how different cities could share the games, how communities could benefit.
Crucially it will also examine how much it could cost as well as assess the chances of a bid succeeding. The Conservative-Lib Dem coalition government said in 2013 it estimated hosting in London had cost £8.9bn.
A report in 2013 by the UK Trade and Investment, which has since been replaced by the Department for International Trade, said it had sparked a £9.9bn boost to the economy through new contracts, sales and foreign investments.
But the estimated amount was queried by some, including the Federation of Small Businesses and the National Institute of Economic and Social Research (NIESR).
The new feasability study for the Northern Games will be done by government, UK Sport, the Northern Mayors and include the British Olympic and Paralympic associations.
Healey said: "Olympic legacy lasts way beyond the celebration of sport over the summer. The North hosting an event as big as this would be truly unforgettable.
"Britain's experience of London 2012 is proof we can host the world. I'm picking up the pace on our work to potentially bid for these prestigious games. It will lift communities, create opportunities and give the UK a huge boost."
News of the funding for the study was welcomed by the British Olympic Association, ParalympicsGB and UK Sport.
"We welcome the government's continued support for exploring the potential of a future bid for the Olympic and Paralympic Games in the UK in the 2040s," they said in a joint statement.
"Building on the success and legacy of London 2012, we look forward to working in partnership to explore this exciting opportunity and the benefits it could deliver for the nation, and for the global Olympic and Paralympic movements."